The critical t statistic (t*) is
the t statistic having degrees of freedom equal to df and a
cumulative probability
equal to the critical probability (p*).

Should you express the critical value as a t statistic or as a z score?
There are several ways to answer this question. As a practical matter,
when the sample size is large (greater than 40), it doesn't make much
difference. Both approaches yield similar results. Strictly speaking,
when the population standard deviation is unknown or when the
sample size is small, the t statistic is preferred. Nevertheless, many
introductory texts and the Advanced Placement Statistics Exam use the
z score exclusively. On this website, we provide sample problems that
illustrate both approaches.